The generator matrix 1 0 0 1 1 1 X 1 X^2+X 1 1 X 1 X^2+X 1 X^2+X 1 1 0 0 X^2 1 1 1 0 X^2 1 1 1 X^2 1 X X 1 1 1 0 1 1 0 1 0 X^2+X 1 1 1 0 X^2 X^2 0 X 1 1 X^2 X 1 1 1 X^2 X^2 1 1 1 1 0 0 1 X 1 0 X 1 X^2+X 1 X^2+X 1 1 1 0 1 0 0 1 X^2+X+1 1 X^2 0 X^2 X^2+X+1 1 X+1 1 0 1 X^2 X^2+X 1 1 X X^2+1 X^2+1 X^2+X 1 X^2+X X^2+1 1 X^2+X+1 1 1 0 1 X X^2+X X^2+X+1 1 X X^2+X 0 1 1 X^2+X X^2+X+1 X 1 1 1 X 1 1 X^2+1 X+1 1 1 X+1 X X+1 1 0 X^2+X+1 X^2+1 X X^2+X+1 X^2+X 0 X 1 X X 1 X+1 1 X^2+1 X^2+X X 0 X^2 0 0 1 1 X+1 0 1 X+1 1 X X+1 X X X+1 X+1 X^2+1 X X^2+X+1 0 1 1 X X^2+1 X^2+X X 1 X^2+X 1 X^2+X+1 X 0 1 X+1 X^2+X+1 X^2+X 0 X^2 1 X^2 1 X^2+1 X+1 1 X^2 X^2 X^2 0 X^2+X 1 X^2 1 X 1 X+1 X^2 X^2+X X^2+1 X^2 X^2+1 1 1 1 X+1 X^2+X+1 1 1 X X^2+X X^2+X 1 1 X^2+X X^2 X^2+X+1 1 X^2 X+1 X 0 0 0 X X X^2+X X^2 X^2+X 0 0 X X^2 X 0 X^2 X^2+X X X^2 X^2+X X X^2 X X X^2+X X^2+X X 0 X^2 X^2 X^2 X^2 X^2+X 0 X^2+X X^2 0 X^2+X X X X^2+X 0 X^2 0 X^2 0 X^2+X X^2 X^2 0 0 0 X 0 0 X X^2+X 0 X^2 X X^2+X X^2+X X^2+X 0 0 X^2+X X X X^2 X^2 X^2 0 X^2 0 X X X^2+X X^2 X^2 0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 70. Homogenous weight enumerator: w(x)=1x^0+100x^70+244x^71+474x^72+418x^73+712x^74+668x^75+736x^76+564x^77+763x^78+554x^79+701x^80+478x^81+528x^82+350x^83+320x^84+156x^85+164x^86+98x^87+56x^88+38x^89+30x^90+6x^91+12x^92+8x^93+5x^94+2x^97+2x^98+4x^100 The gray image is a linear code over GF(2) with n=312, k=13 and d=140. This code was found by Heurico 1.16 in 3.95 seconds.